Sandys cuts got rid of 'most of the trash that had been hanging round after the war' - so not really painful, and the Battleships (didn't PoW and Repulse and Renown show that the day of the Battleship was well and truly dead, anyway?) and the reserves. The RN was left leaner than before, probably more efficient, and with a committment to its future. As you argue, Mountbatten turned the 57 Defence WP to the RN's advantage.
By bloated, I was referring to the scores of frigates and destroyers which were necessary only to support an Empire role which was clearly disappearing. The Navy in '57 was larger than its Cold War responsibilities and commitments required.
The Air Force was left much smaller, and has never, since 57, been more than a token force, capable of doing no more than buying time before inevitable nuclear escalation in the Cold War, and of delivering Armageddon to a handful of Soviet cities.
If money was no object, and were we spending 6% of GDP on defence I'd be an enthusiastic supporter of carriers. I might even admit that a European carrier force might be a useful tool, if spreading the costs that way would work. But in these times of extreme budgetary pressure, they just do not cut it as a cost effective solution. Moreover, in these times, when military operations require political and international supports, the basing flexibility they appear to offer is often illusory. If you can't get basing in a neighbouring nation, you probably can't conduct the op anyway. If you want to keep SHar and carriers you need to come up with an alternative 'big ticket' cut - like Trident or all UK armour or all fixed wing land-based offensive support and attack FJs.